The second derivative of a family of functions is given by

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

f_k''(x)=k e^{-x^{2}}-1

, where

k

is a real parameter. For which of the following is the corresponding function concave down on its entire domain? (a)

0<k<1

(b)

k<1

(c)

k\le 1

(d)

k>1